Total probability theorem:
|
Partition of Sample-Space:
Take a sample space 'S'. Let A1, A2, L An be the
set of the mutually exclusive and exhaustive set of sample space S.
These A1, A2, L, An events are said to partition the
Sample space in to 'n'-parts.
We have 
And 
|
|
The total Probability Theorem:
Let 'A' be any event of S. We can write 
are mutually exclusive,
would also be mutually exclusive.
This is called as the total probability of the event A.
Remark:
- P(A/Ai) gives up contribution of Ai in occurrence of A.
Example: One bag has 4 white balls and 3 black balls and a 2nd bag contains 3 white balls and 5 black balls. One ball is drawn from 1st bag and placed unseen in the 2nd bag. What is the probability that a ball now drawn from 2nd bag is black ?
Sol: Bag - I Bag - II
4 w 3 w
3 B 5 B
Let A1 be the event that white ball is transferred from bag - I to bag - II and A2 be the event that black ball is transferred from bag - I to bag -II.
P (A1) =4/7, P(A2) = 3/7
Let 'A' be probability the finally a black ball is drawn from the 2nd bag P(A/A1) = 5/9, P(A/A2) = 6/9.
Now from the total probability theorem we get,
P(A) = P(A1) . P(A/A1) + P(A2) . P(A/A2) = 
Email based Total probability theorem Assignment Help -Total probability theorem Homework Help
We at www.expertsmind.com offer email based Total probability theorem assignment help - homework help and projects assistance from k-12 school level to university and college level and engineering and management studies. We provide finest service of Mathematics assignment help and Mathematic homework help. Our experts are helping students in their studies and they offer instantaneous tutoring assistance giving their best practiced knowledge and spreading their world class education services through e-Learning program.
Expertsmind's best education services
- Quality assignment-homework help assistance 24x7 hrs
- Best qualified tutor's network
- Time on delivery
- Quality assurance before delivery
- 100% originality and fresh work